子系统状态相容性与凸几何
Compatibility of subsystem states and convex geometry
摘要：
子系统相容性问题是关于一组子系统状态是否与整个系统的状态相容的问题，已经得到了很多研究。在这里，我们从一个新的角度来解决这个问题，利用凸性的思想，已成功地对可分性问题。类似于纠缠见证，我们引入了相容见证的概念，并证明了这些对象的一些性质。我们表明，子系统的兼容性问题可以解决数值和有效地使用半定规划，从这个解决方案的数值结果可以用来提取精确的分析结果，一个想法，我们用来反驳一个猜想的子系统问题的Butterley等人。[Found.Phys.3683（2006）]。最后，我们考虑如何的想法可以被用来解决一些重要的变种的兼容性问题，特别是，被认为是相同的粒子（称为N-表示费米子的情况下）的情况下。
英文摘要：
The subsystem compatibility problem, which concerns the question of whether a set of subsystem states are compatible with a state of the entire system, has received much study. Here we attack the problem from a new angle, utilising the ideas of convexity that have been successfully employed against the separability problem. Analogously to an entanglement witness, we introduce the idea of a compatibility witness, and prove a number of properties about these objects. We show that the subsystem compatibility problem can be solved numerically and efficiently using semidefinite programming, and that the numerical results from this solution can be used to extract exact analytic results, an idea which we use to disprove a conjecture about the subsystem problem made by Butterley et al. [Found. Phys. 36 83 (2006)]. Finally, we consider how the ideas can be used to tackle some important variants of the compatibility problem; in particular, the case of identical particles (known as N-representability in the case of fermions) is considered.
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